Should clubs focus on shot quality using expected goals?

By Dan Altman, creator of smarterscout

Lately I've seen a lot of scuttlebutt, both serious and sarcastic, suggesting clubs have neglected long shots because of an obsession with expected goals. There's even been an academic paper purporting to show that players should take more long shots. I think there are problems with the premises of these discussions, so I'll try to establish some basic facts without resorting to fancy mathematical methods.

First, expected goals do not always relate directly to the distance from goal. Our models of shot quality take a whole host of attributes into account: distance, angle, body part used, phase of play, preceding actions, etc. As a result, shots the same distance from goal can have very different expected goals. Importantly, shorter shots can have lower expected goals than longer shots.

Have a look at this map of shots in open play by Kasper Dolberg – scorer of a shot from outside the box in Euro 2020 – while he was at Ajax:

We use different colours to denote ranges for expected goals. Dolberg took shots from outside the box that were red, orange... and blue. The central area just outside the box has higher expected goals, on average, than the widest areas inside the box. You can see shots taken from inside the box that were red – wide angles and headers – as well as shots in virtually the same locations with much higher expected goals. These differences stem from the events leading to the shot.

So a club trying to increase its shot quality doesn't need to focus only on location; it needs to focus on situation as well. If a club makes a rule that no player is allowed to shoot from outside the box, then its players might take a lot of low-quality shots from wide areas inside the box. Or they might pass up good chances to score stemming from advantageous situations outside the box.

It's worth noting that even these conclusions might miss the point. If a club's objective is the highest possible position in the league table, then its players ought to make decisions that maximise the points taken from each match – wherever those decisions might take them. For instance, if the choice is between shooting and losing possession, then shooting is probably the right choice, regardless of expected goals.

Over the course of a season, however, clubs can and do make tactical choices that affect shot quality. And here's where we come to the big questions: Is increasing shot quality even a good idea, or is there too much of a tradeoff between quality and quantity? Have data-driven clubs taken the focus on expected goals too far?

In these sorts of analyses, it's often helpful to look at the data in the simplest possible way. I like to start with summary statistics – for example, what were the average expected goals per shot in the Premier League for the past five seasons? I don't even need a table to tell you; the answer was 0.11 expected goals per shot in each season. So there hasn't been a noticeable change in shot quality recently, at least in England's top tier.

Now I'll drill down a level by graphing clubs' expected goals per shot against their total expected goals. If clubs were going too far with a maniacal focus on shot quality, then we might expect to see a sort of parabola here. Improving expected goals per shot might help total expected goals for a while, but then it would start to hurt. Yet that's not what we see, at least not in the Premier League:

Though a few clubs have high expected goals per shot and low total expected goals, the overall relationship is a pretty positive one (ρ = 0.65). There just doesn't seem to be an obvious tradeoff between shot quality and shot quantity.

Yet the chart above tells only part of the story. Every squad is different, so we really want to know what will happen if a specific club's shot quality rises or falls, whether incidentally or deliberately. Here's another chart with the same axes, tracking the paths of the clubs that spent consecutive seasons in the Premier League:

I've marked the paths as follows: green arrows show clubs where expected goals per shot and total expected goals rose or fell together, and white arrows show clubs where one fell while the other rose. In other words, the white arrows show where clubs may have pushed too far on shot quality (the arrows pointing southeast) or may have dialed back after pushing too far (the arrows pointing northwest). The green arrows show where a focus on shot quality made more sense.

There are a lot more green arrows than white ones, so again there's not too much evidence of a widespread and excessive focus on shot quality. But a lot of arrows are also pretty flat, suggesting that the quality-quantity tradeoff is alive and well at some clubs.

Perhaps the most interesting paths above are those in the northeast corner. Four clubs increased their total expected goals markedly while reducing expected goals per shot. The changes in shot quality were small, so a causal link seems unlikely. But it's still worth asking what happened at Manchester United in 2017-18, Arsenal and Liverpool in 2018-19, and Manchester City in 2020-21.

The fact that these clubs experienced similar changes in different seasons is interesting, too. In a more detailed study, I'd want to account for the quality of defending and other factors that might have influenced expected goals across the league and at specific clubs. For now, though, this evidence hints that a focus on expected goals is still worth considering for the majority of clubs.

[Technical note: Mathematically inclined readers will know that in a scenario with a perfect quality-quantity tradeoff, clubs should usually choose quality. Take a situation where you can choose five shots with 0.2 expected goals or two shots with 0.5 expected goals. With three points for a win and one point for a draw, scoring five goals is unlikely to add many points; the key is to score the first goal. So quality wins, albeit only by a little bit. I posted some earlier work on this topic here, which also links to an empirical study of the tradeoff.]

[Photo: warrenski]

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